The main approach to pest control consists in the application of chemical insecticides. The efficacy of insecticides is reduced due to the development of resistance by pest populations. This is an especially important problem with the Colorado potato beetle. There are different strategies for the use of insecticides to slow the formation of resistance. Based on the results of long-term studies, we propose a hypothesis on delaying the development of resistance by applying insecticides at low doses. To test this hypothesis, we built predictive discrete genetic models of resistance in the Colorado potato beetle populations. The model based on the classical equations of population genetics has been supplemented by various factors. Calculations of the survival rates of individuals of the Colorado potato beetle were carried out taking into account the statistical regularities of the distribution of toxic substance after treatment by insecticides. We calculated the survival rates for different genotypes using a lognormal distribution after at least doubling the insecticide dose. The factor of differential mortality during winter was additionally introduced into the model. The use of phenetic markers of nonspecific resistance to environmental factors allowed us to compute the model with mediated intergenic interactions. Various hypotheses on the strategies of overcoming resistance have been tested using this model. The calculations demonstrated that use of insecticides at the minimum effective dose (low dose) leads to a slower increase in the proportion of resistant individuals in the populations of the Colorado potato beetle for two seasons. Resistance develops much more slowly following alternate treatment with insecticides from different chemical classes. The best strategy is through off-season treatment with lower doses of insecticides of different chemical classes.